I have replaced a ceiling light and the three-way switch and the 3-way dimmer that operate it. Now the light is on constantly no matter whether switches are on or off? I am pretty sure the common wires a re correct. Any suggestions?

Try switching the red and black on the common. It depends on whether the switch was through wired or used as a switch loop.

Tried that but no change. I don't know much about these things, but is there any way other than mis-wiring that this could happen? I accidentally blew the circuit while working on this. Could I have somehow caused a short or something?

Tried that but light stays on. I don't know much about these things, but is there any way the power could stay on even if this is wired correctly? I accidentally tripped the circuit breaker in the process of doing this. Could I have shorted out a wire or something? Would that cause this?

is there any way the power could stay on even if this is wired correctly?

No, if wired correctly the lights will switch off.

The hot (black) from the power source is connected to the common of one switch. The hot (black) to the light is connected to the common of the other switch. You didn't say where the power source is. It is likely that the power source is the first light fixture and that you have a switch loop. If that is correct it is likely that your error is in the first fixture where you connected the switch loop to the power source.

The power source runs into the first switch (the dimmer) and I have it connected to the common terminal of the dimmer. Does it matter which of the remaining terminals the two travelers are attached to? I thought I tried them both, but can go back and switch them if it will help. I thought that with the power hooked up to the first switch I could go to the second switch and, with the first switch in up position, see which of the three wires in the second switch has power, then change the position of the first switch and see which of the other wires in the second switch has power, and the one that doesn't have power in either position is the common wire for that switch. All well and good, and there is indeed a wire that has no power in either position. The trouble is that both of the other two wires have power no matter what position the first switch is in. Does that seem right?

Does it matter which of the remaining terminals the two travelers are attached to?

No, it does not matter which wires are connected to the traveler screws.

If you indeed have the black from the power source connected to the common of the first switch (the dimmer) and the travelers of the first switch connected to the travelers of the second switch the light should turn off. If you are mistaken about which terminals are common there should still be a combination of switch settings that turns the light off.

I suspect that there is something else wrong. If you indeed do have power coming to the switch box there should be one 2-wire cable and one 3-wire cable in each switch box. The black of the 2-wire cable in each box should be connected to the common, the whites of the 2-wire cables should be connected to the white of the 3-wire cable. The red and black of the 3-wire cable should be connected to the traveler screws of each switch.

There is a way of wiring a set of 3-way switches in which you have a 2-wire cable and a 3-wire cable on one box and only a 3-wire cable in the other.

Tell me how many wires in each switch box and I will draw a diagram of the wiring.

Each switch box has three wires. The power originally comes in up at the light box. It connects to other lights in other rooms. This wiring was done long ago, but if I remember correctly a 3-wire cable runs from the light box down to the dimmer switch and another 3-wire cable runs from the light box down to the other switch. The hot to the dimmer switch is attached to the hot that runs from the circuit board and continues to the rest of the run. The other two (traveler) wires from the first 3-wire cable attach to like wires in the second 3-wire cable. The remaining wire in the second 3-wire cable runs from the second switch to the light. Does this make sense? I am replacing this light and both switches, but this is a wiring setup that has worked for years with the old light.

OK, makes more sense now. By 3 wires I take it you mean one 3-wire cable to each box. Give me a few minutes to make a drawing.

Note that I revise drawing to change colors of wires between switches. Does not make any difference electrically but make easier to follow.

Thanks. I think this looks about like I have it, but I'll have to investigate this further this evening or tomorrow morning. Thanks for taking the time to do this.